Topological Quantum Field Theory (TQFT) is a branch of theoretical physics and mathematics that explores the relationships between quantum field theory and topology, a branch of mathematics that studies properties of space that are preserved under continuous transformations. ### Key Concepts of TQFT: 1. **Quantum Field Theory (QFT)**: - QFT is a framework for constructing quantum mechanical models of subatomic particles in particle physics. It combines classical field theory, special relativity, and quantum mechanics.
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A quantum field theory assigning vector spaces to closed spatial manifolds and linear maps to interpolating spacetime cobordisms, compatibly with composition and disjoint union. Its TQFT partition function on is the trace of the identity of the state space on , hence its dimension.